distances, which form the subject of road books. In establishing the nautical mile of our distinguished Navigators as the mile of Landsmen also, it appeared proper to alter the length of the chain from 22 yards, to some aliquot part of the nautical mile. By adopting 10 fathoms of the new measure as the precise length of the new chain, which is also to be subdivided into 100 links like the former, the link will become exactly the tenth part of the fathom. Hence all distances that are to be expressed in fathoms, but which do not involve an integral number of fathoms, may be most conveniently stated in fathoms and tenths. For example, I would state the distance of a battery as being equal to 1057.9 fathoms, or to 1057 fathoms 9 links, in preference to stating it as 1057 fathoms, 5 feet, 4 digits; and as all distances for itinerary purposes are best measured in chains and links, the surveyor will thus be enabled to state them in aliquot parts of the same instrument, with which he measures them.

(12) A very great disadvantage, attending our present lineal measure, will be removed by adopting the new system proposed. When we hear such a distance as 47,565 yards mentioned, it is quite impossible to form any idea, how many English miles it is equal to, without performing a very troublesome calculation in Arithmetical Reduction. In like manner, no one knows how many yards are contained in 79 miles and 3 quarters, and very few persons could even guess at the probable number, without putting pencil to paper, and multiplying the mixed number 79 into the number 1760, which is a very troublesome process.

By the new system suggested, this embarrassing uncertainty, as to the comparative value of the greater and lesser denominations of itinerary measure, will be completely done away, as the value in miles of a given number of fathoms will be known at once, without the necessity of calculation, and without even an effort of the mind. Thus, for example, 83,760 fathoms will be known as being equal to 83 miles and 760 fathoms, or a very little more than 83 miles and 3 quarters: and, vice versa, 157 miles and a half will, in like manner be known, as it were by intuition, to be 157,500 fathoms. Every one must admit the vast importance of this improvement.

(13) According to the present custom of this country, as before mentioned, the foot is used exclusively for all architectural and mechanical measurements, which however are afterwards reduced by calculation to a much more

complex form; whilst all itinerary distances are stated in some higher denomination, such as yards, rods, furlongs, or miles; and I believe that in some districts fathoms are also used, although this is less common. It will have been ob

served (in Article 6) that I propose to retain the same principle, which is a very judicious one, but with the advantage of greater simplicity, by using the foot exclusively as the unit for all measurements of the former kind, and the fathom for the latter.

(14) The rod of 5 yards is, of all our English measures, the most objectionable, it being useless as a lineal measure; and indeed as such nearly obsolete, it having been superseded by the Surveyor's chain. Unfortunately it has been retained as an element of all our superficial measures, applied to which it causes a vast deal of unnecessary trouble for no purpose upon earth. Such a measure as the rod, which was originally a long pole cut in a wood, and which is incommensurate with the two next lower denominations the yard and the foot, and a most awkward multiple of the inch, is only worthy of those days of feudal ignorance, in which the standard of English lineal measure was referred to the average length of a barleycorn, and the standard of weight to the average weight of a dry grain of wheat, from the middle of the ear.*

(15) In the table of our present long measure before stated, I inserted the barleycorn, merely for the purpose of pointing out the absurdity of the practice of almost all our Elementary Writers on Arithmetic, in retaining that obsolete subdivision of the inch, in teaching which to their readers, as well as in teaching the Flemish ell, and the French ell, as parts of English cloth measure, they have been teaching superfluity or error. If the third part of an inch were a measure in common use, it would be the most inconvenient of all possible subdivisions of that dimension, but as it is never used at all, it is perfectly ridiculous to insert it in a table of English measures; and yet I have never seen it omitted in any, excepting in those which are given in the Almanac of the Society for the diffusion of Useful Knowledge.

* Dr. Kelly states, in his Universal Cambist, that besides the statute pole of 5 yards or 16 feet, there is the Woodland pole of 18 feet, the rope of 20 feet, the pole plantation measure of 21 feet, the Cheshire pole of 24 feet, and the Sherwood pole of 25 feet. So far as regards the practice of the most eminent Architects, Builders and Surveyors in this country, the pole is entirely obsolete as a measure of length or distance, for they never use it in actual measurements, only in calculation.

(16) For architectural purposes, the present English foot is always subdivided into 96 equal parts, namely, into inches and eighths, and this system is universally adopted by Architects and Builders, and by all the Mechanics employed under their superintendence, who lay out the minuter parts of their work by a 2 feet rule of 24 inches, subdivided in the above manner. But when they come to measure their work, in order to find quantity and value, they are obliged to use the duodecimal instead of the octaval divisions of the inch. Now to plan and mark out work by inches and eighths, and afterwards to estimate the value of the same by inches and twelfths, is evidently an inconsistency, which might be got rid of to a certain degree, by subdividing the English foot into inches and twelfths, like the old French foot. But there is an objection to this arrangement, inasmuch as the English foot is so much smaller than the French, that the duodecimal divisions of the English inch would be too minute, and as it were crowded together, and therefore not so clear and distinct to the eye, as is desirable. Hence although the superior 2 feet English rules, made of ivory for the use of Architects, &c. have their inches on one side usually divided into eighths, and on the other side into twelfth parts; the latter are never used in practice, and by inspecting both, it will be seen, that they are much less clear than the former. On another side of the same scales, it is also common to divide the inches into tenth parts, and this system of dividing the inch has been exclusively adopted by Gagers or Revenue Officers, in their calculations; although in their measurements, they do not use the common Mechanic's 2 feet rule, but a much longer sliding rule, by which they not only measure, but occasionally perform their calculations; as is also done by Timber-measurers, who use a sliding rule similar in principle, but graduated differently, so as to suit their own business. But it would be superfluous to enlarge further upon sliding rules of any description, as these form no part of the common measures of the country, to which our present subject is confined.

(17) Besides the three modes of subdividing the English foot that have been stated, namely, into inches and eighths for laying out Artificers' work, into inches and tenths for the gaging of casks, &c., and into inches and twelfths for calculating the measurements of Artificers' work; it is proper to observe, that the system of subdividing the foot into 100 equal parts, which has been recom

mended by me in preference to any of the above, is not altogether a novelty in this country; it having been already adopted by all our Civil Engineers, in taking levels, for the purpose of laying out Canals, Railways, or Roads. In planning any portion of a road in particular, it is absolutely necessary to determine the proportional slope, which can only be done, by dividing some measured distance by the difference of level between its two extreme points. If for example we suppose the difference of level between any two points, that are 377 feet 9 inches distant from each other, to be exactly 15 feet 8 inches, before we can fix any proportion between these two dimensions, they must both be reduced to eighths of an inch, by which we obtain the two numbers 36264 and 1511, and the former being divided by the latter, yields 1 foot in 24 as the slope due to the above measurements. Hence every such question, if stated in feet and inches, involves two operations in Arithmetical Reduction, and one in Long Division. By rejecting the inch altogether, and adopting the decimal subdivisions of the foot, these calculations are of course very much simplified, since the distance may be divided by the height at once; and thus the troublesome process of the two arithmetical reductions is saved. The decimal subdivisions of the foot tend no less to simplify and abreviate all calculations dependent upon the measurement of Artificers' work; as will be explained in some of the following articles, and this important advantage is the chief reason, that induced me to recommend the abolition of the inch and its parts.

(18) If the subdivisions of the proposed new foot, thus divided into hundredth parts, be compared with those of the present English foot, as divided into inches and eighths, they will be found so very nearly equal, that the former will be almost as distinct and clear to the eye as the latter, from which they only differ by about one thirty-sixth part in defect.

(19) It will have been observed, that in the new Table of lineal measure before given (Article 6), I have omitted the hand. The abolition of this measure will simplify, to a certain degree, as it is certainly best to measure the height of horses, and of all other animals, in feet and parts of a foot, according to the more accurate practice of the scientific Zoologists of this country, who never make use of the hand of the horse dealers.

(20) We will next proceed to Cloth Measure.

OF THE PRESENT ENGLISH CLOTH MEASURE.

4 Nails (of 24 inches each)

3 Quarters

4 Quarters

5 Quarters

6 Quarters

.....

1 Quarter of a Yard. •1 Flemish Ell.

....1 Yard.

1 English Ell.

1 French Ell.

In respect to the above form, in which English Cloth Measure is usually stated in books, it is so far incorrect, that the French Ell so styled is imaginary, since it does not agree with the Aune or Ell used in France; and although the same objection does not apply to the Flemish ell, which either is or was very nearly equal to three quarters of an English yard, yet it appears absurd to load the memory, with the name of a measure never used in this country at all. Indeed the English ell itself has become obsolete as a measure, for the word ell is never mentioned between Drapers and their Customers, except when a piece of cloth is about one yard and a quarter in width, when it is usually termed Ell-wide.

(21) It may appear almost superfluous for me to point out, that the practice of measuring Artificers' work, and of measuring cloth, are entirely different in this country; and the same difference exists in all countries. The working Mechanic requires the use of a short measure like the foot, very accurately and minutely subdivided. The Draper, on the contrary, requires as his unit of measure, a longer dimension, such as the yard or ell, suited to the human arms, not stretched out to their full length, but very moderately extended so as to handle the cloth without over exertion. All nations have their peculiar standards of Cloth Measure, which generally vary from about 21 to 27 inches in length, except in France, where the Aune was nearly equal to 47 inches of English measure: but in some parts of the South of France, and of Spain and in Italy, the Canne, a much longer measure, varying from about 5 to nearly 8 English feet in length, was used for this purpose. The English yard appears to be a proper medium between those extremes, for the shorter measures must give unnecessary trouble by too many repetitions, whilst the longer ones cannot be handled so conveniently. Under these considerations I have given up the idea, which at first occurred to me, of measuring cloth in future by the foot, using for that purpose a 3 feet measure, not to be termed the yard. This arrangement would so far have simplified the proposed system of lineal